Method and system for regulating a stability control system of a vehicle

ABSTRACT

The invention proposes a method for regulating a stability control system of a vehicle based on the forces acting at the center of each wheel of the vehicle. The actions of the driver, i.e. steering, acceleration or braking, produce forces (changes in forces) are transmitted by the tires to the ground. Control of the operating means of the vehicle (active anti-roll device, engine torque, braking torque, load per wheel or direction) utilizes instructions resulting from the actions of the driver to apply forces. The invention proposes a method of expressing, in terms of forces, the inputs of the driver as a function of the inertia of the vehicle body, velocity of forward movement of the vehicle, and angle at the steering wheel (steering wheel velocity and steering wheel acceleration). If the actual forces that are measured do not correspond to the forces desired by the driver, the active system compensates for this difference by acting on the force distributions in the chassis.

BACKGROUND AND SUMMARY OF THE INVENTION

The present invention relates to systems for controlling the stabilityof a vehicle, commonly known as ESP (Electronic Stability Program)systems.

In safety systems for vehicles it is necessary to be able to assess thebehavior of the vehicle in real time. This is the basis of the so-calledESP systems for controlling stability. These systems currently rely on,inter alia, monitoring movements of the vehicle by installing sensors tomeasure the transverse acceleration of the vehicle and the yaw rate ofthe vehicle.

When moving under good safety conditions, that is, when the stability ofthe vehicle is not compromised, the vehicle obeys the driver's commands.If the driver, basically as a result of his handling of the steeringwheel, drives the vehicle beyond the limits of stability, the vehiclewill exhibit oversteering or understeering. The vehicle turns, that is,performs a yaw movement, in excess of that desired by the driver(oversteering) or less than desired by the driver (understeering).

Using a mathematical model of the tire and a mathematical model of thevehicle, and based on measurements supplied by sensors recording theactions of the driver of the vehicle (angle relative to the steeringwheel, application of the brakes and accelerator) and speed sensors forthe wheels, and from measurements of the transverse acceleration and yawrate, an ESP system constantly calculates the forces at the center ofthe wheels and estimates the grip potential of the road surface as afunction of the transverse acceleration. Furthermore, the ESP systemevaluates the behavior of the vehicle, compares it to the behaviordesired by the driver, and corrects this behavior if it establishes thatthe vehicle is not moving along a stable path.

However, the use of tire models can introduce a certain number ofapproximations into the overall model. Furthermore, the fact that acontrol system is based on the displacements of the vehicle necessarilyleads to a response a posteriori, which can be effective only after adelay depending on the inertia of the vehicle. It can be seen from thisthat an ESP system, since its variables of state include measurements ofthe transverse acceleration and the yaw rate of the vehicle, first ofall has to measure the displacement of the vehicle before decidingwhether the displacement is within the bounds of stability or not, andcan only then act on the operating means of the vehicle. Moreover, thecurrently available ESP system observes only the movements of the bodyof the vehicle without knowing specifically the exact reasons for theloss of control. The movements of the body of the vehicle are caused bycontact between the tire and the ground.

The system will detect a displacement of the vehicle not in accord withthe command given by the driver, more slowly the greater the inertia ofthe vehicle, and the necessary correction will be all the more difficultthe greater the inertia. At the present time the operating means arebasically the vehicle's brakes, controlled in this case wheel by wheeland outside the voluntary action of the driver, and the motive force,which can be reduced automatically by regulating the engine.

Furthermore, the detection of yaw movements requires the use of costlysensors. Also, existing systems have to estimate the grip of the wheelson the road surface in order to select the actuating parameters. Thisestimation deviates to a greater or lesser degree from the actualconditions.

The object of the present invention is to obviate the aforementioneddisadvantages and, more particularly, to exclude completely the inertiaof a vehicle in order to be able to act on the appropriate operatingmeans so as to maintain the vehicle in a stable path in accordance withthe driver's commands, by regulating the operating means in such a waythat the actual forces acting at the center of each wheel correspond tothe desired forces.

The invention provides a vehicle stability control system and a methodfor controlling the stability of a vehicle that have the advantage thatthey can be carried out without having to measure the yaw angle of thevehicle.

The invention relates to a vehicle comprising a body and at least onefront ground contacting arrangement and at least one rear groundcontacting arrangement, each ground contacting arrangement comprising ineach case one wheel, each wheel comprising a pneumatic or non-pneumatictire in contact with the ground, the vehicle having a characteristictime that is a function of its inertia and corresponds to the time phaseshift in the manifestation of the cornering forces on the wheels in thefront and in the rear, following a command from the driver of thevehicle, the vehicle being provided with operating means to act on theforces transmitted to the ground by each of the wheels.

In a vehicle the steering of the wheels produces a cornering force atthe front, a movement of the vehicle body, followed by a cornering forceat the rear. The cornering force of the rear wheel or wheels thusintervenes with a slight delay with respect to the command on thesteering wheel. In order to establish more precisely the actionsrequired to correct the path, the invention proposes to take intoaccount this delay T as explained hereinafter.

According to a first aspect of the invention, the method comprises thefollowing steps:

-   -   (a) measuring in real time the actual value of one variable        selected in the group of the cornering force “Y” and the        vertical load “Z” acting at the center of each of the front and        rear wheels;    -   (b) calculating in real time the desired value of at least one        reference parameter, said at least one reference parameter being        correlatable to the actual value, as a result of an action of        the driver on the operating means and taking into account the        load transfers on both sides of the mid plane of symmetry of the        vehicle;    -   (c) comparing said desired value of the reference parameter of        step (b) to the actual value to determine whether the actual        value is compatible with the desired value of the reference        parameter; and    -   (d) if the comparison of step (c) indicates that the actual        value is not compatible, acting on the operating means such that        the actual value is brought into substantial compatibility with        the desired value of the reference parameter.

A preferred aspect relating to the specific application of the inventionto vehicles each of whose axles comprises at least two ground contactingarrangements each comprising one wheel, is described hereinafter, theground contacting arrangement being mounted on either side of themid-plane of symmetry of the vehicle. This is the conventionalarrangement in a four-wheeled touring vehicle. However, the invention isalso applicable to two-wheeled vehicles, such as motorbikes, being notedthat in this case the inertia of the body is considerably lower. Eachground contacting arrangement comprises a wheel, generally having atire, which in this description means a pneumatic tire or non-pneumatictire, in contact with the ground. The vehicle is provided with operatingmeans to act on the forces transmitted to the ground by each of thewheels, such as brakes, means for steering the wheels, optionallyselectively wheel by wheel, and distribution of the loads carried byeach of the wheels.

The commands of the driver of the vehicle are intended to maintain thevehicle on a straight line path regardless of the ambient disturbances(for example sidewind gusts, change of the road grip on all or part ofthe vehicle), or are intended to cause the vehicle to execute atransverse displacement (change of lane for overtaking on a motorway) orto turn. Regardless of the operating means of the vehicle that areactuated by the driver (conventional steering wheel, operating lever asillustrated for example in patent application EP 0 832 807), thedriver's wish in fact is to exert specific cornering forces or specificchanges of these cornering forces.

The invention thus proposes to measure in real time the effectivecornering forces, compare them to commands of the driver translated intocornering forces or changes in cornering forces, and thereby to controlappropriate operating means available on the vehicle. In a firstparticular embodiment, said variable is the cornering force “Y” and saiddesired value of at least one reference parameter of step (b) is thedesired cornering force “Y_(d)” at the center of each wheel. Moreparticularly, step (c) further comprises generating an error signalrepresentative of the magnitude and direction of the difference betweenthe actual and desired cornering forces and step (d) comprisescontrolling said operating means to minimize said error signal.

In another particular embodiment, said variable is the cornering force“Y”, said operating means including a command for controlling thesteering, step (a) comprises calculating in real time the effective yawmoment corresponding to the actual cornering forces “Y”, said desiredvalue of at least one reference parameter of step (b) being the desiredyaw moment, step (a) comprises measuring in real time a signal at thesteering command and calculating the desired yaw moment “M_(d)”, andstep (c) comprises utilizing said desired yaw moment “M_(d)” forcomparison with the effective yaw moment of step (a). More particularly,step (c) further comprises generating an error signal representative ofthe magnitude and the direction of the difference between the effectiveyaw moment and the desired yaw moment “M_(d)”; and step (d) comprisescontrolling said operating means to minimize said error signal.

Accordingly, if the cornering force of the front axle has beensaturated, the vehicle will understeer since the cornering forces of thefront train are less than the forces desired by the driver (desiredforces meaning forces corresponding to the actions by the driver on hissteering wheel or on other steering commands available). An automaticaction, for example of the type already known per se in conventional ESPsystems (other types of actions will be discussed hereinafter) enables aresultant force to be exerted on the vehicle chassis in accordance withthe driver's wishes and thus enables understeering to be avoided.

If on the other hand it is the cornering force of the rear axle thatfirst becomes saturated, then the vehicle will oversteer since thecornering forces of the rear train are less than the forces desired bythe driver. The automatic action enables a resultant force to be exertedon the vehicle chassis in accordance with the driver's wishes and thusenables oversteering to be avoided.

The above description refers to what is conventionally called thestationary state (or steady state). When considering a typical transientstate involved in an emergency maneuver (avoiding an obstacle, changinglane), the speed of engagement of the steering wheel may be regarded asequivalent to a desired yaw moment acting on the vehicle. If the actualyaw moment is less than the desired yaw moment, the vehicle will notturn sufficiently. If on the other hand the actual yaw moment is greaterthan the desired yaw moment, the vehicle will turn too much.

According to yet another particular embodiment, said variable is thevertical load “Z”. More particularly, said operating means including acommand for controlling the steering, and said desired value of at leastone reference parameter of step (b) being the desired load “Z_(d)” atthe center of each of the front and rear wheels, the method comprises astep for measuring in real time a signal at the steering command andcalculating the desired loads “Z_(d)”. More particularly, step (c)further comprises generating an error signal representative of themagnitude and the direction of the difference between the actual loads“Z” and the desired loads “Z_(d)”; and step (d) comprises controllingsaid operating means to minimize said error signal.

The method according to the invention permits, if the cornering forcesof one of the axles do not correspond to the desired cornering forces,or if the effective yaw moment is greater than the desired yaw moment,or if the vertical loads do not correspond to the desired verticalloads, the transmission of an action signal to the operating means inorder to minimize the error signal without the need to establish such asignal, without the need to measure the yaw rate of the vehicle. Ofcourse, such a method is compatible with measuring the yaw rate,particularly if it is desired to add redundancy terms to thecalculations.

As can be seen, the invention provides a method for regulating a systemfor controlling the stability of a vehicle based on the forces acting atthe center of each wheel of the vehicle. More specifically, the actionsof the driver, whether they involve steering, accelerating or braking,will be reflected in forces (changes in forces) transmitted by the tiresto the ground. Depending on whether or not these force variations arecompatible with respect to the commands of the driver, it may beconcluded whether or not the vehicle is stable. The origin of futuredisplacements is found starting from the forces acting on the ground. Inthis way it is possible to correct the path of the vehicle much soonerand an ESP system, or more generally a stability control system, gainsin fineness of correction. Both the safety and comfort of the driver andpassengers are improved.

The estimation of stability criteria in real time, based on forcesacting on the ground, enables the stability control of the path of avehicle to be improved, the direct measurement of the force enabling,for example, the saturation point of the tire on each of the wheels tobe monitored accurately regardless of the grip on the road surface, bydetecting the occurrence of non-linearity between the developedcornering force and the sideslip angle of the tire in question, as wellas non-linearity of the developed cornering force and the load appliedto the tire.

The cause of loss of stability of the vehicle is mainly the fact thatthe tires are no longer able to correct the path, given the movement ofthe vehicle. Irrespective of the cornering force developed by the tires,this will never be able to counteract the forces of inertia. This may bedue to a poor grip (wet road, (black) ice, snow, sand, dead leaves), tothe fact that the tire is used by the driver under improper conditions(flat tire or underinflated tire), or to the fact that the vehicle isdirectly placed in a situation of excessive drift or sideslip thatexceeds the physical limits of one or more of the tires. In this case itmay be said that one or more of the tires reaches its saturation point.

The suspension bearings may be equipped with instruments, as proposed inpatent application JP60/205037, which enables the longitudinal andtransverse forces developed by the tire to be recognized easily bymeasurements made on the suspension bearings. Alternatively, the tireitself is equipped with sensors for recording the forces of the tire onthe ground. A measurement may for example be made as explained in patentDE 39 37 966 or as discussed in U.S. Pat. No. 5,864,056 or in U.S. Pat.No. 5,502,433.

On the basis of the forces measured by one or other of the abovemethods, and from equilibrium equations of a ground contactingarrangement, the forces acting at the center of each wheel mayaccordingly easily be calculated. Thus, in real time 3 forces X, Y and Zare available, which in particular enables the Y or Z signal to beprocessed for the reasons explained in the present document.

The invention also relates to vehicle stability control systems, saidvehicle having a body and at least one front ground contactingarrangement and at least one rear ground contacting arrangement, eachground contacting arrangement comprising in each case one wheel, eachwheel comprising a pneumatic or non-pneumatic tire in contact with theground, the vehicle having a characteristic time that is a function ofits inertia and corresponds to the time phase shift in the manifestationof the cornering forces on the wheels in the front and in the rear,following a command from the driver of the vehicle, the vehicle beingprovided with operating means to act on the forces transmitted to theground by each of the wheels, such as brakes, means for steering thewheels. The system further comprises:

-   -   (a) means for measuring in real time the actual values of one        variable selected in the group of the cornering force “Y” and        the vertical load “Z” acting at the center of each of the front        and rear wheels;    -   (b) a controller allowing to calculate in real time the desired        values of at least one reference parameter, said at least one        reference parameter being correlatable to the actual values, as        a result of an action of the driver on the operating means and        taking into account the load transfers on both sides of the mid        plane of symmetry of the vehicle, said controller allowing to        perform comparisons between the desired values with the measured        actual values in order to obtain an error signal, and;    -   (c) means for acting on the operating means so as to minimize        the error signal.

According to various aspects, as explained hereabove for the method forcontrolling the stability of a vehicle, the variable can be the actualcornering force “Y” in which case the reference parameter can be eitherthe desired cornering force “Y_(d)” or the desired yaw moment “M_(d)”,or said variable is the vertical load “Z” and the reference parameter isthe desired loads “Z_(d)”.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described in more detail hereinafter with the aidof the accompanying figures, in which:

FIG. 1 is a block diagram illustrating a system in accordance with theinvention,

FIG. 1A shows schematically a car featuring the system according to theinvention,

FIG. 2 shows the arrangement of a two-wheeled vehicle and frame ofreference,

FIG. 3 a shows the arrangement of a four-wheeled vehicle and frame ofreference;

FIG. 3 b is a side view of a four-wheeled vehicle of FIG. 3 a;

FIG. 3 c is a front view of a four-wheeled vehicle of FIG. 3 a;

FIG. 4 shows the linearized cornering stiffness curve;

FIGS. 5 a-c, 6 a-d, and 7 a-d illustrate the forces resulting from asteering command in the form of an increasing sinusoidal curve, on a wetsurface at 90 km/hour, in which,

FIG. 5 a illustrates the front axle cornering force,

FIG. 5 b illustrates the rear axle cornering force,

FIG. 5 c illustrates the yaw moment,

FIG. 6 a illustrates the left front load,

FIG. 6 b illustrates the right front load,

FIG. 6 c illustrates the left rear load,

FIG. 6 d illustrates the right rear load,

FIG. 7 a illustrates the left front cornering force,

FIG. 7 b illustrates the right front cornering force,

FIG. 7 c illustrates the left rear cornering force, and

FIG. 7 d illustrates the right rear cornering force;

FIGS. 8 a-c, 9 a-d, and 10 a-d illustrate the forces resulting from asteering command in the form of a increasing sinusoidal curve, on a wetsurface at 90 km/hour for a vehicle equipped with means for controllingthe anti-rolling distribution, in which,

FIG. 8 a illustrates the front axle cornering force,

FIG. 8 b illustrates the rear axle cornering force,

FIG. 8 c illustrates the yaw moment,

FIG. 9 a illustrates the left front load,

FIG. 9 b illustrates the right front load,

FIG. 9 c illustrates the left rear load,

FIG. 9 d illustrates the right rear load,

FIG. 10 a illustrates the left front cornering force,

FIG. 10 b illustrates the right front cornering force,

FIG. 10 c illustrates the left rear cornering force, and

FIG. 10 d illustrates the right rear cornering force;

FIG. 11 illustrates the differences of path between a vehicle withcontrol (reference numeral 2) of the anti-rolling distribution and avehicle without control of the anti-rolling distribution (referencenumeral 1) in a maneuver involving a steering command in the form of anincreasing sinusoidal curve, on a wet surface at 90 km/hour,

FIG. 12 illustrates the anti-rolling distribution in order to stabilizethe vehicle;

FIGS. 13 a-c, 14 a-d, and 15 a-d illustrate the forces resulting from anavoidance maneuver, on a wet surface, at 90 km/hour, leading to adestabilization of the vehicle, in which,

FIG. 13 a illustrates the front axle cornering force,

FIG. 13 b illustrates the rear axle cornering force,

FIG. 13 c illustrates the yaw moment,

FIG. 14 a illustrates the left front load,

FIG. 14 b illustrates the right front load,

FIG. 14 c illustrates the left rear load,

FIG. 14 d illustrates the right rear load,

FIG. 15 a illustrates the left front cornering force,

FIG. 15 b illustrates the right front cornering force,

FIG. 15 c illustrates the left rear cornering force, and

FIG. 15 d illustrates the right rear cornering force;

FIGS. 16 a-c, 17 a-d, and 18 a-d illustrate the forces resulting from anavoidance maneuver, on a wet surface, at 90 km/hour, for a vehicleequipped with a control of the anti-rolling distribution, in which

FIG. 16 a illustrates the front axle cornering force,

FIG. 16 b illustrates the rear axle cornering force,

FIG. 16 c illustrates the yaw moment,

FIG. 17 a illustrates the left front load,

FIG. 17 b illustrates the right front load,

FIG. 17 c illustrates the left rear load,

FIG. 17 d illustrates the right rear load,

FIG. 18 a illustrates the left front cornering force,

FIG. 18 b illustrates the right front cornering force,

FIG. 18 c illustrates the left rear cornering force, and

FIG. 18 d illustrates the right rear cornering force;

FIG. 19 illustrates the path differences between a vehicle with control(reference numeral 2) of the anti-rolling distribution and a vehiclewithout control of the anti-rolling distribution (reference numeral 1),in this avoidance maneuver, on a wet surface, at 90 km/hour;

FIG. 20 illustrates the anti-rolling distribution in order to stabilizethe vehicle.

DETAILED DESCRIPTION

We shall start from the fact that, at a given velocity, an angle at thesteering wheel imposed by the driver may be interpreted as a corneringforce or load instruction, or as a yaw moment instruction on thevehicle. This is shown diagrammatically in the upper part of FIG. 1.Furthermore, it has been seen that in order to implement the presentinvention, it is necessary to have measurements of the actual corneringforces (cornering forces of the tires or elastic tire casings used inthe ground contacting arrangement). This is illustrated in the left-handsection, starting from “vehicle,” in FIG. 1. In the case where it isdesired to act on the distribution of the loads (see other explanationsbelow concerning the effect on the yaw moment of the distribution of theloads), it is necessary to have measurements of the actual loads.

The diagram in FIG. 1 superimposes several methods: either the actionsof the driver at a given moment and the preceding actions areinterpreted as a demand for cornering forces, which are compared to thecornering forces measured at the center of the wheel, or the actions ofthe driver and the preceding actions are interpreted as a demand forchanges in load, which are compared to the loads measured at the centerof the wheel, or alternatively, the actions of the driver areinterpreted as a demand for a yaw moment, and the cornering forcemeasurements made at the center of the wheel are converted into ameasured yaw moment in order to make the required comparison. Thedifferences found by a comparator enable a controller to decide on thenecessary correction by acting on the operating means so as to stabilizethe vehicle and make it follow the instructions of the driver.

In a vehicle, the steering of the wheels results in a cornering force ofthe front axle, a movement of the vehicle body, followed by a corneringforce of the rear axle. The cornering force of the rear axle thus occurswith a slight delay with respect to the command on the steering wheel.In order to be able to determine the path correction actions moreaccurately, the invention proposes to take account of this delay.

The instruction values of the cornering forces then depend on the actionon the steering command at the present instant t and at the instant tminus the delay associated with the inertia of the vehicle (termed T).This delay time depends only on the characteristics of the vehicle(inertia, wheelbase) and the sideslip rigidities of its pneumaticsuspension. An expression for this delay time is:$T = \frac{I_{Vehicle}V}{{l_{1}^{2}D_{F}} + {l_{2}^{2}D_{R}}}$where

-   -   V is the instantaneous velocity of the vehicle;    -   I_(vehicle) is the inertia of the vehicle undergoing yaw (also        referred to as Iz);    -   L1 is the distance from the front axle to the center of gravity;    -   L2 is the distance from the rear axle to the center of gravity;        and,    -   D_(F), D_(R) are the sideslip rigidities of the front and rear        axles (sum of the sideslip derivatives of the tires of the same        axle).

It is assumed that the cornering forces of the front train are less thanthe forces required by the driver (as determined by his actions on thecommands). An automatic action enables a resultant force on the vehiclechassis to be obtained in accordance with the wishes of the driver andthus enables understeering to be avoided.

The various operating means that may be actuated include, of course, thebrakes. As an alternative or in addition to a braking action, an actionon a supplementary steering means, exerted for example by means of anirreversible stepping motor mounted in the steering column, also enablesthe resultant forces on the vehicle chassis to be approximated inaccordance with the wishes of the driver. Another possible way ofeffecting the action on a steering means consists for example in sendingthe appropriate control commands to the controller described in U.S.Pat. No. 5,884,724.

As an alternative or as a further addition to braking actions or actionson the steering mentioned above, an action on the distribution of theanti-roll device between the front axle and rear axle also enablesaction to be exerted on the cornering forces developed respectively bythe front and rear axles. This involves altering the load supported byeach wheel by modifying the distribution of the overall load (unchanged)between the wheels, fully taking account of the load transfer to theouter wheels when steering or cornering.

In fact, when a vehicle departs from the path desired by the driver, oneor other or several of the tires become incapable of developing theexcess cornering force that they would have had to develop in order tocompensate for the forces of inertia. It may be said that the tire ortires have reached their saturation limit. More specifically, thissaturation phenomenon, when it starts, involves for most of the time asingle tire of a single axle. As a result one of the axles becomesincapable of developing the expected cornering force and the vehiclewill oversteer or understeer depending on whether the saturationinvolves the rear axle or the front axle.

Furthermore, it is known that when steering, the centrifugal forceoverloads the outer tires. The distribution of this overload between thefront axle and rear axle depends on the anti-roll characteristics of thevehicle suspension.

By reducing the share of anti-rolling force developed by the axlecontaining the tire whose cornering force reaches saturation pointfirst, not only can the other tire on the same axle develop a greatercornering force due to a larger vertical load, but also the saturationpoint of a tire on the other axle will be approached or even reached,thereby setting a limit on or reducing the cornering forces developed bythe other axle.

If on the other hand it is the cornering force of the rear axle thatreaches saturation point first, the vehicle oversteers because thecornering force forces of the rear train are less than the forcesdesired by the driver. An automatic braking action or action on asupplementary steering means or on the anti-roll distribution enables aresultant forces to be obtained on the vehicle chassis in accordancewith the wishes of the driver and thus enables oversteering to beavoided.

FIG. 2 shows a representation of a two-wheeled vehicle according to acommonly adopted simplification employed also for modeling four-wheeledvehicles. The center of gravity of the vehicle is denoted by CG, thelongitudinal axis of the vehicle connecting the front wheel (turned) andthe rear wheel and passing through the center of gravity (axis CGx). Thesum of the cornering forces Y_(F), Y_(R) acting on the wheels of eachaxle in question is translated to the center of each axle. The angle δthat the velocity vector makes with respect to the longitudinal axis ofthe vehicle, and the yaw rate ψ of the vehicle around the vertical axisof the vehicle are shown. The distance between the front axle (andrespectively the rear axle) and the center of gravity CG is denoted byl₁ (respectively l₂). Such a diagram already enables interesting resultsto be obtained.

However the invention proposes, in order to determine more accuratelythe correction actions on the path, to take account of the forces on theground wheel by wheel. In the center of an axle a comparison of thecornering forces of each wheel and the desired cornering forces enablesthe cause of saturation of the overall arrangement of the axle to bedetermined exactly and thus enables more effective correction actions tobe selected.

FIG. 3 a shows diagrammatically a four-wheeled vehicle, with a center ofgravity CG. Neither the angle δ that the velocity vector makes withrespect to the longitudinal axis of the vehicle, nor the yaw angle ψ areshown, so as not to complicate the diagram. The four-wheeled model iscloser to the vehicle in the sense that it takes into account the forceson the centers of the four wheels and expresses the lateral loadtransfers associated with the engagement of the anti-roll device of thevehicle when steering. The four-wheeled model is accordingly morecomplete than the two-wheeled model and more accurately reflects theaction of the load transfers on the dynamics of the vehicle. The loadson each of the four tires are represented by Zp1, Zp2, Zp3 and Zp4. Thecornering forces (or lateral forces) acting on each of the wheels areidentified by the reference numerals Yp1, Yp2, Yp3 and Yp4.

FIG. 3 b shows the rolling axis R of the vehicle, the height h of thecenter of gravity CG with respect to the ground, the height h₁ of therolling axis R with respect to the ground in the vertical plane passingthrough the center of the areas of contact of the tires of the frontaxle with the ground, and the height h₂ of the rolling axis with respectto the ground in the vertical plane passing through the center of theareas of contact of the tires of the rear axle with the ground. Thefour-wheeled model is based on the assumption of a sprung mass MSresting on 2 axles. This sprung mass is able to rotate about the rollingaxis R.

FIG. 3 c shows the oversteering moment of the vehicle caused by the loadtransfer in the transverse direction, K₁ and K₂ representing theanti-rolling rigidities on respectively the front axle and the rearaxle. In the diagram “v1” denotes the front track of the vehicle and“v2” denotes the rear track of the vehicle.

The monitoring of the four supports and error signals generated betweenthe desired cornering forces and actual cornering forces enables thefour supports to be optimized by acting in an appropriate manner on theoperating means, as will be explained hereinafter.

The procedure for controlling the operating means described above areshown diagrammatically in the “Controller” box in FIG. 1, which controlsthe one or more “operating means” discussed above.

The above paragraphs refer to what is commonly known as the stationarystate (or the steady state). Considering a typical transient state of anemergency maneuver (avoiding an obstacle, changing lane), the speed ofactuation of the steering wheel is instead regarded as equivalent to adesired yaw moment on the vehicle. If the actual yaw moment is less thanthe desired yaw moment, the vehicle does not turn sufficiently. If theactual yaw moment is greater than the desired yaw moment, the vehicleturns excessively. The controller then acts in an appropriate manner onone or other or several of the possible operating means including thebrakes, or on a supplementary steering means or on the distribution ofthe anti-rolling system, thereby enabling a yaw moment to be exerted onthe vehicle chassis in accordance with the wishes of the driver.

The following conventional expressions will be adopted:

-   -   Desired front axle cornering force: Y_(F)d    -   Desired rear axle cornering force: Y_(R)d    -   Desired cornering force of the tires: Yp_(1,2,3,4)d    -   Desired load on each tire: Zp_(1,2,3,4)d    -   Desired yaw moment: M_(z d)    -   ψ yaw angle of the vehicle    -   δ sideslip angle of the vehicle    -   α_(c) steering angle of a wheel    -   γt transverse acceleration    -   D_(1,2,3,4) the sideslip rigidities of the tires    -   D_(F) and D_(R) the sideslip rigidities of the front and rear        axles

A two-wheeled vehicle will first of all be discussed hereinafter (seeFIG. 2).

The equations of the two-wheeled vehicle are as following:Mγ _(t) =MV({dot over (δ)}+{dot over (ψ)})=Y _(F) +Y _(R)  (1)where M is the mass of the vehicle, V is the longitudinal velocity ofthe vehicle, Y_(F) is the cornering force on the front axle, and Y_(R)is the cornering force on the rear axle, equation (1) expressing thefact that the cornering forces balance out the transverse acceleration,I _(z) {umlaut over (ψ)}=l ₁ Y _(F) −l ₂ Y _(R)  (2)where I_(z) is the yaw inertia, l₁ is the distance from the front axleto the center of gravity, l₂ is the distance from the rear axle to thecenter of gravity, equation (2) expressing the fact that the moments arein equilibrium.

The rigid body movement of the two-wheeled vehicle and the steering ofthe wheels of the front axle enables the sideslips of the front and reartires to be expressed as follows: $\begin{matrix}\begin{matrix}\text{Sideslip of the front train::} & {\delta_{F} = {\delta + {l_{1}\frac{\overset{.}{\psi}}{V}} - \alpha_{C}}}\end{matrix} & (3) \\\begin{matrix}\text{Sideslip of the rear train:} & {\delta_{Arr} = {\delta - {l_{2}\frac{\overset{.}{\psi}}{V}}}}\end{matrix} & (4)\end{matrix}$

The quantity l1 (respectively l2) is the distance from the front axle(respectively rear axle) to the center of gravity CG of the vehicle. Thegeometry of the vehicle is shown in FIG. 2.

These sideslips of the tires give rise to cornering forces on thetwo-wheeled vehicle:Y _(F) =−D _(F)δ_(F)  (5)Y _(R) =−D _(R)δ_(R)  (6)

By substituting the equations 3 and 4 in 5 and 6, one obtains$\begin{matrix}{Y_{F} = {- {D_{F}\left( {\delta + {l_{1}\frac{\overset{.}{\psi}}{V}} - \alpha_{C}} \right)}}} & (7) \\{Y_{R} = {- {D_{R}\left( {\delta - {l_{2}\frac{\overset{.}{\psi}}{V}}} \right)}}} & (8)\end{matrix}$

By substituting the equations (7) and (8) in the equations (1) and (2),a system is obtained that is expressed only as a function of the yawrate (and its derivative), the sideslip angle (and its derivative), andthe characteristics of the vehicle: $\begin{matrix}{{{MV}\left( {\overset{.}{\delta} + \overset{.}{\psi}} \right)} = {{D_{F}\left( {\delta + \frac{l_{1}\overset{.}{\psi}}{V} - \alpha_{c}} \right)} + {D_{R}\left( {\delta - \frac{l_{2}\overset{.}{\psi}}{V}} \right)}}} & \left( {1\quad{bis}} \right) \\{{I_{z}\overset{¨}{\psi}} = {{l_{1}\left( {D_{F}\left( {\delta + \frac{l_{1}\overset{.}{\psi}}{V} - \alpha_{c}} \right)} \right)} - {l_{2}\left( {D_{R}\left( {\delta - \frac{l_{2}\overset{.}{\psi}}{V}} \right)} \right)}}} & \left( {2\quad{bis}} \right)\end{matrix}$

By a Laplace transform it is possible to express the transfer functionsbetween the yaw rate and the angle at the steering wheel, and betweenthe body sideslip and the angle at the steering wheel. The static part(that is to say the part relating to a zero frequency) of this transferfunction is then simply expressed as a function of the characteristicsof the vehicle (coefficient of proportionality) and of the forwardmovement velocity: $\begin{matrix}{\overset{.}{\psi} = {\frac{1}{l_{1} + l_{2}}\frac{V}{1 + \frac{V^{2}}{\frac{D_{F}{D_{R}\left( {l_{1} + l_{2}} \right)}^{2}}{M\left( {{D_{R}l_{2}} - {D_{F}l_{1}}} \right)}}}\alpha_{c}}} & (9) \\{\delta = {\frac{1}{l_{1} + l_{2}}\frac{l_{2} - \frac{l_{1}{MV}^{2}}{D_{R}\left( {l_{1} + l_{2}} \right)}}{1 + \frac{V^{2}}{\frac{D_{F}{D_{R}\left( {l_{1} + l_{2}} \right)}^{2}}{M\left( {{D_{R}l_{2}} - {D_{F}l_{1}}} \right)}}}\alpha_{c}}} & (10)\end{matrix}$

These expressions may be simplified by introducing a quantity Vc, calledcritical velocity, which is comparable to a velocity and depends on thecharacteristics of the vehicle (weight supported by the front axleM_(F), weight supported by the rear axle M_(R), distances l1 and l2) andits pneumatic mounting: $\begin{matrix}{V_{c}^{2} = {\frac{D_{F}{D_{R}\left( {l_{1} + l_{2}} \right)}^{2}}{M\left( {{D_{R}l_{2}} - {D_{F}l_{1}}} \right)} = {\frac{D_{F}{D_{R}\left( {l_{1} + l_{2}} \right)}}{{D_{R}M_{F}} - {D_{F}M_{R}}} = \frac{l_{1} + l_{2}}{\frac{M_{F}}{D_{F}} - \frac{M_{R}}{D_{R}}}}}} & (11)\end{matrix}$

The expressions (9) and (10) become:$\overset{.}{\psi} = {\frac{1}{l_{1} + l_{2}}\frac{V}{1 + \frac{V^{2}}{V_{c}^{2}}}\alpha_{c}}$$\delta = {\frac{1}{l_{1} + l_{2}}\frac{l_{2} - \frac{l_{1}{MV}^{2}}{D_{R}\left( {l_{1} + l_{2}} \right)}}{1 + \frac{V^{2}}{V_{c}^{2}}}\alpha_{c}}$

These expressions may be reintroduced into the equations (3) and (4) andthen into the equations (5) and (6) in order to obtain the forcesdesired by the driver: $\begin{matrix}{{Y_{F}{desired}} = {\frac{M_{F}}{l_{1} + l_{2}}\frac{V^{2}}{1 + \frac{V^{2}}{{Vc}^{2}}}\alpha_{c}}} & (12) \\{{Y_{R}{desired}} = {\frac{M_{R}}{l_{1} + l_{2}}\frac{V^{2}}{1 + \frac{V^{2}}{{Vc}^{2}}}\alpha_{c}}} & (13)\end{matrix}$

It can be seen that these formulae express the fact that the corneringforce demand resulting from the actions of the driver depends only onthe command (α_(c)) itself, on the velocity of the vehicle (V) and onother parameters, all of which are functions of the vehicle itself (thatis to say describe the vehicle).

Finally, by differentiating equation (9) and multiplying the yawacceleration by the yaw inertia, one obtains the desired yaw moment Mz:$\begin{matrix}{\overset{¨}{\psi} = {\frac{1}{l_{1} + l_{2}}\frac{V}{1 + \frac{V^{2}}{{Vc}^{2}}}{\overset{.}{\alpha}}_{c}}} & \quad \\{{M_{Z}{desired}} = {{I_{Z}\overset{¨}{\psi}} = {\frac{I_{z}}{l_{1} + l_{2}}\frac{V}{1 + \frac{V^{2}}{{Vc}^{2}}}{\overset{.}{\alpha}}_{c}}}} & (14)\end{matrix}$

Similarly, formula (14) expresses the fact that the yaw moment demandresulting from the actions of the driver depends only on the command(α_(c)) itself, on the velocity of the vehicle (V) and on otherparameters, all of which are functions of the vehicle itself (that is tosay describe the vehicle).

It is also possible to express the changes of commands at the steeringwheel as demands for changes of forces in the trains: $\begin{matrix}{{{\overset{.}{Y}}_{F}{desired}} = {\frac{M_{F}}{l_{1} + l_{2}}\frac{V^{2}}{1 + \frac{V^{2}}{{Vc}^{2}}}{\overset{.}{\alpha}}_{c}}} & (15) \\{{{\overset{.}{Y}}_{R}{desired}} = {\frac{M_{R}}{l_{1} + l_{2}}\frac{V^{2}}{1 + \frac{V^{2}}{{Vc}^{2}}}{\overset{.}{\alpha}}_{c}}} & (16) \\{{{Y_{R}{{desired}(t)}} = {\frac{M_{R}}{1 + \frac{V^{2}}{V_{c}^{2}}}\frac{V^{2}}{l_{1} + l_{2}}{\alpha_{c}\left( {t - T} \right)}}}{{{\overset{.}{Y}}_{R}{{desired}(t)}} = {\frac{M_{R}}{l_{1} + l_{2}}\frac{V^{2}}{1 + \frac{V^{2}}{{Vc}^{2}}}{{\overset{.}{\alpha}}_{c}\left( {t - T} \right)}}}} & (17)\end{matrix}$

The instruction at the instant t depends on the steering command at theinstant t−T. This delay, which is associated with the yaw inertia of thevehicle, appears as a characteristic time of the vehicle in equation (2bis). /${I_{z}\overset{¨}{\psi}} = {{l_{1}\left( {D_{F}\left( {\delta + \frac{l_{1}\overset{.}{\psi}}{V} - \alpha_{c}} \right)} \right)} - {l_{2}\left( {D_{R}\left( {\delta - \frac{l_{2}\overset{.}{\psi}}{V}} \right)} \right)}}$${{I_{z}\overset{¨}{\psi}} - {\frac{{l_{1}^{2}D_{F}} + {l_{2}^{2}D_{R}}}{V}\overset{.}{\psi}}} = {{\left( {{l_{1}D_{F}} - {l_{2}D_{R}}} \right)\delta} - {l_{1}D_{R}\alpha_{c}}}$

The yaw time constant is thus: $\begin{matrix}{T = \frac{I_{Z}V}{{l_{1}^{2}D_{F}} + {l_{2}^{2}D_{R}}}} & (18)\end{matrix}$

It is assumed that it is possible to measure at each instant thecornering forces Y for all the wheels, the variations of the corneringforces Y, and the variations of angle at the steering wheel. It isproposed to actuate a path control system as soon as the differencebetween the desired forces and the actual measured forces becomes toolarge. The criterion of stability that is thus proposed expresses thefact that the vehicle remains stable as long as this difference is small(compromise between the wishes of the driver and the actual conditions).

This criterion of stability takes into account the fact that thecornering force of the tire reaches saturation point either because thetire is no longer in a straight line with the sideslip, or because thetire is no longer in a straight line with the applied load. In order tobe able to detect this double saturation more readily, it is assumedthat the tire is in a straight line with respect to both the load andthe sideslip. This linearization is illustrated in FIG. 4. Thecontinuous line represents a real curve giving the value of thecornering stiffness of a tire as a function of the load applied to thetire, and the dotted line, plotted according to the linearizationassumption, gives the value of the cornering stiffness of a tire as afunction of the load applied to the tire. It can be seen that thedifference with respect to reality increases as the saturation point(load saturation) of the tire is approached. Furthermore, the linearmodel representing the cornering stiffness of the tire with respect tothe load should give results comparable to the actual state of affairsclose to the operational point so as not to trigger a system undernormal driving conditions (see meeting point of the continuous curve anddotted line curve). The proposed solution consists in modeling atheoretical tire that would have a linear cornering stiffness (dottedstraight line curve), forming a tangent to a real cornering stiffnesscurve at the static operating point M_(F) g/2, that is to say withouttransfer of load.

By linearizing the expression for the cornering stiffness of a tire onthe front axle, we obtain: $\begin{matrix}{{D_{1}\left( {Zp}_{1} \right)} = {D_{1,0} + {\left( \frac{\partial D_{1}}{\partial Z} \right)_{0}\left( {{Zp}_{1} - \frac{M_{F}g}{2}} \right)}}} & (19)\end{matrix}$ $\frac{\partial D}{\partial Z}$is the sensitivity of the cornering stiffness to the transfer of load inthe vicinity of the static load M_(F) g/2. This sensitivity at the frontis denoted A1 and at the rear is denoted A2. D_(1,0) is the corneringstiffness of the front tire under a static load M_(F) g/2

The cornering stiffness of a front tire thus takes the form:$\begin{matrix}{{D_{1}\left( {Zp}_{1} \right)} = {D_{1,0} + {A_{1}*\left( {{Zp}_{1} - \frac{M_{F}g}{2}} \right)}}} & \left( {19\quad{bis}} \right)\end{matrix}$

The cornering stiffness of a rear tire thus takes the form:${D_{3}\left( {Zp}_{3} \right)} = {D_{3,0} + {A_{2}*\left( {{Zp}_{3} - \frac{M_{R}g}{2}} \right)}}$

Similarly, the suspension is modeled by linear relationships giving loadtransfers under a permanent regime. The following notations are adoptedto describe the suspensions:

-   -   Ms sprung weight of the vehicle;    -   K1 rigidity of the front anti-rolling bar;    -   K2 rigidity of the rear anti-rolling bar;    -   h1 height of the front axle rolling center;    -   h2 height of the rear axle rolling center;    -   h height of the center of gravity;    -   V1 track of the front train; and,    -   V2 track of the rear train.

These notations are illustrated in FIGS. 3 a, 3 b, 3 c.

By means of the expressions for the desired cornering forces, and usingthe linear suspension model, the discounted load transfer on axle 1 is:$\begin{matrix}{{\Delta\quad Z_{F}\quad{desired}} = {{\frac{1}{v_{1}}\left\lbrack {\frac{K_{1}h}{K_{1} + K_{2} - {M_{S}{gh}}} + {\frac{M_{F}}{M_{S}}h_{1}}} \right\rbrack}\frac{M_{S}}{1 + \frac{V^{2}}{V_{c}^{2}}}\frac{V^{2}}{l_{1} + l_{2}}\alpha_{c}}} & (20)\end{matrix}$

Furthermore, the vehicle body movements are delayed with respect to thesteering wheel steering, with a delay time given by expression (18).$\begin{matrix}{{\Delta\quad Z_{F}\quad{{desired}(t)}} = {{\frac{1}{v_{1}}\left\lbrack {\frac{K_{1}h}{K_{1} + K_{2} - {M_{S}{gh}}} + {\frac{M_{F}}{M_{S}}h_{1}}} \right\rbrack}\frac{M_{S}}{1 + \frac{V^{2}}{V_{c}^{2}}}\frac{V^{2}}{l_{1} + l_{2}}{\alpha_{c}\left( {t - T} \right)}}} & \left( {20\quad{bis}} \right)\end{matrix}$

On the tires of the front train the instruction load is thus the sum ofthe static load on a quarter of the vehicle and the load transfer on theaxle.${{Zp}_{1}\quad{desired}} = {\frac{M_{F}g}{2} + {\Delta\quad Z_{Av}\quad{desired}}}$${{Zp}_{2}\quad{desired}} = {\frac{M_{F}g}{2} - {\Delta\quad Z_{F}\quad{desired}}}$

On the front train the expected vertical loads are: $\begin{matrix}{{{Zp}_{1}\quad{{desired}(t)}} = {\frac{M_{F}g}{2} + {{\frac{1}{v_{1}}\left\lbrack {\frac{K_{1}h}{K_{1} + K_{2} - {M_{S}{gh}}} + {\frac{M_{F}}{M_{S}}h_{1}}} \right\rbrack}\frac{M_{S}}{1 + \frac{V^{2}}{V_{c}^{2}}}\frac{V^{2}}{l_{1} + l_{2}}{\alpha_{c}\left( {t - T} \right)}}}} & (21) \\{{{Zp}_{2}\quad{{desired}(t)}} = {\frac{M_{F}g}{2} - {{\frac{1}{v_{1}}\left\lbrack {\frac{K_{1}h}{K_{1} + K_{2} - {M_{S}{gh}}} + {\frac{M_{F}}{M_{S}}h_{1}}} \right\rbrack}\frac{M_{S}}{1 + \frac{V^{2}}{V_{c}^{2}}}\frac{V^{2}}{l_{1} + l_{2}}{\alpha_{c}\left( {t - T} \right)}}}} & \left( {21\quad{bis}} \right)\end{matrix}$

On the rear train the expected vertical loads are: $\begin{matrix}{{{Zp}_{3}\quad{{desired}(t)}} = {\frac{M_{R}g}{2} + {{\frac{1}{v_{2}}\left\lbrack {\frac{K_{2}h}{K_{1} + K_{2} - {M_{S}{gh}}} + {\frac{M_{R}}{M_{S}}h_{2}}} \right\rbrack}\frac{M_{S}}{1 + \frac{\quad_{V^{2}}}{V_{c}^{2}}}\frac{V^{2}}{l_{1} + l_{2}}{\alpha_{c}\left( {t - T} \right)}}}} & (22) \\{{{Zp}_{4}{{desired}(t)}} = {\frac{M_{R}g}{2} - {{\frac{1}{v_{2}}\left\lbrack {\frac{K_{2}h}{K_{1} + K_{2} - {M_{S}{gh}}} + {\frac{M_{R}}{M_{S}}h_{2}}} \right\rbrack}\frac{M_{S}}{1 + \frac{V^{2}}{V_{c}^{2}}}\frac{V^{2}}{l_{1} + l_{2}}{\alpha_{c}\left( {t - T} \right)}}}} & \left( {22\quad{bis}} \right)\end{matrix}$

Knowing the load on each tire, by linear modeling of the tire (equation19 bis) the instruction cornering force on each of the four tires can bededuced:Yp ₁desired=−D ₁(Zp ₁desired)*δ_(F)desired

From equations (3), (4), (9) and (10) the desired tire sideslips are:$\begin{matrix}{{\delta_{R}{{desired}(t)}} = {{- \frac{\frac{M_{R}}{D_{R}}}{1 + \frac{V^{2}}{V_{c}^{2}}}}\frac{V^{2}}{l_{1} + l_{2}}{\alpha_{c}(t)}}} & (23) \\{{\delta_{R}{{desired}(t)}} = {{- \frac{\frac{M_{R}}{D_{R}}}{1 + \frac{V^{2}}{V_{c}^{2}}}}\frac{V^{2}}{l_{1} + l_{2}}{\alpha_{c}\left( {t - T} \right)}}} & (24)\end{matrix}$

By using the expressions for the cornering stiffness (19 bis), thedesired load (21) and the desired tire sideslip (23), the instructioncornering force is then: $\begin{matrix}{{{Yp}_{1}{{desired}(t)}} = {\frac{D_{1,0} + {A_{1}\left( {{{Zp}_{1}{{desired}(t)}} - \frac{M_{R}g}{2}} \right)}}{D_{R}}\frac{M_{F}}{1 + \frac{V^{2}}{V_{c}^{2}}}\frac{V^{2}}{l_{1} + l_{2}}{\alpha_{c}(t)}}} & (25) \\{{{Yp}_{2}{{desired}(t)}} = {\frac{D_{2,0} + {A_{1}\left( {{{Zp}_{2}{{desired}(t)}} - \frac{M_{F}g}{2}} \right)}}{D_{R}}\frac{M_{F}}{1 + \frac{V^{2}}{V_{c}^{2}}}\frac{V^{2}}{l_{1} + l_{2}}{\alpha_{c}(t)}}} & \left( {25{bis}} \right)\end{matrix}$

Similarly, on the rear axle and taking into account the delay in thecornering force of the rear axle, we have: $\begin{matrix}{{{Yp}_{3}{{desired}(t)}} = {\frac{D_{3,0} + {A_{2}\left( {{{Zp}_{3}{{desired}(t)}} - \frac{M_{R}g}{2}} \right)}}{D_{R}}\frac{M_{R}}{1 + \frac{V^{2}}{V_{c}^{2}}}\frac{V^{2}}{l_{1} + l_{2}}{\alpha_{c}\left( {t - T} \right)}}} & (26) \\{{{Yp}_{4}{{desired}(t)}} = {\frac{D_{4,0} + {A_{2}\left( {{{Zp}_{4}{{desired}(t)}} - \frac{M_{R}g}{2}} \right)}}{D_{R}}\frac{M_{R}}{1 + \frac{V^{2}}{V_{c}^{2}}}\frac{V^{2}}{l_{1} + l_{2}}{\alpha_{c}\left( {t - T} \right)}}} & \left( {26\quad{bis}} \right)\end{matrix}$

It is assumed that the cornering forces Y for all the wheels, thevariations of the cornering forces Y, and the variations of the angle atthe steering wheel can be measured at each instant in time. It isproposed that a path control system be triggered as soon as thedifference between the desired forces and the actual measured forcesbecomes too large. The criterion of stability that is thus proposedexpresses the fact that the vehicle remains stable as long as thisdifference remains small (compromise between the wishes of the driverand the actual conditions).

The advantage of detecting these differences on each wheel is that thesystem knows more precisely the reason for the loss of control of thevehicle.

A simulation of the dynamic behavior of a vehicle under typicalmaneuvers is presented with the aid of the following figures. Thesimulation model that is used is a four-wheeled model with 7 degrees offreedom, enabling the equilibrium of the vehicle to be expressed interms of yaw, pitch, roll and rotation of the four wheels. The foursimulations presented here relate to a vehicle whose characteristics arethose of a Volkswagen Golf car travelling at a speed of 90 km/h.

In the first simulation (FIGS. 5 a-c, 6 a-d, and 7 a-d), a sinusoidalpulse of frequency 0.5 Hz of increasing amplitude and on a wet surfaceis plotted as a steering wheel instruction. This maneuver leads to theloss of control of the vehicle. In all the figures illustrating tirecornering forces (Yp), the axle cornering forces (Y_(F), Y_(R)), theloads (Zp) or yaw moments (Mz) the continuous curves, denoted by “A”,represent the actual values, while the dotted curves, denoted by “D”,represent the values desired by the driver.

In FIGS. 5 a, 5 b, and 5 c the plotted curves show the differencebetween the sum of the two cornering forces of a train (front train orrear train according to the indices “F” or “R” of the figures) and theforce desired by the driver, in the context of formulae (12), (13) and(14). The saturation of the forces of the tire with respect to thedriver's expectations and the phase difference between the actual forcesand the expected forces can be noted.

In FIGS. 6 a, 6 b, 6 c, and 6 d the differences between the actual loadsand the loads desired by the driver as expressed by the formulae (21),(21 bis), (22) and (22 bis) can be seen. In FIGS. 7 a, 7 b, 7 c and 7 dthis loss of control is detected via the saturation of the observedcornering forces of the tires as the difference between the instructioncornering forces expressed by the formulae (25), (25 bis), (26) and (26bis) and the actual cornering forces. At the same time it is found thatthe actual forces are delayed with respect to the instruction,illustrating the phase difference between the intervention of the driverand the reactions of the vehicle. In each case the reference “A”represents the actual forces (continuous line) and the reference “D”refers to the instruction expressed by the proposed method (dottedline).

In the second simulation (FIGS. 8 a-c, 9 a-d, 10 a-d, 11 and 12) it isshown how a modification of the front/rear anti-rolling distribution,controlled as explained above, enables the path of the vehicle to bestabilized. The maneuver is identical to the previous maneuver (steeringcommand in the form of an increasing sinusoidal curve on a wet surfaceat 90 km/h). As soon as excessive yaw forces are detected, theanti-rolling device is reinforced at the front of the vehicle and isreduced by the same amount at the rear so as to make the vehicle stableas quickly as possible and to utilize in the best possible way thegripping potential of the four tires. The saturation of the corneringforces is better controlled and permits smaller phase differences, whichmeans that yaw moments are better handled and vehicle body changes aremore readily identified. To reiterate, in each case the reference “A”represents the actual forces (continuous curve) and the reference “D”refers to the instruction expressed by the proposed method (dottedcurve).

FIGS. 8 a, 8 b, and 8 c show the actual and desired cornering forces ofthe front axle, the rear axle, and the yaw moment of the vehicle. FIGS.9 a, 9 b, 9 c, and 9 d show the actual and desired vertical loads Zp onthe four tires. FIGS. 10 a, 10 b, 10 c, and 10 d show the actual anddesired lateral cornering forces Yp on the four tires.

Although the anti-rolling dynamic distribution does not enable thesaturation of the tire to be avoided completely under the existinggripping conditions, it nevertheless enables the error signal to beminimized and the delay between the commands of the driver and theresponses of the vehicle to be reduced (FIGS. 9 a-d, 10 a-d).

FIG. 11 symbolizes the vehicle (represented by a rectangle) on theaforedescribed path by its center of gravity (shown as a continuousline). In this representation the alignment of the vehicle is shown viathe angle that the vehicle makes with the path. The phase differencebetween the actual alignment of the vehicle and the desired path may beobserved by recording, in specific successive positions illustrated inFIG. 11, the more or less large angle between the orientation of thevehicle and the tangent to the path at the center of gravity of thevehicle until loss of control of the vehicle supervenes due tooversteering.

This loss of control may be anticipated by the difference between thedesired yaw moment and the actual yaw moment. The actual yaw moment ismuch too large and causes the vehicle to swerve, as is shown by the path(FIG. 11). By making the driver's instructions responsive to the forces,such as described by the proposed method, the vehicle remains stable andfollows the path desired by the driver (reference numeral 2, FIG. 11).

FIG. 12 illustrates the anti-rolling distribution in order to stabilizethe vehicle. If a saturation is observed, an anti-roll force is exertedon the rear axle in order to increase the front anti-roll whilemaintaining constant the overall anti-roll stiffness. This change indistribution of the loads stabilizes the vehicle by causing it toundersteer more.

In the third simulation (FIGS. 13 a-c, 14 a-d, and 15 a-d), the driverchanges lane on a wet road surface and loses control of the vehicle. Ineach case the reference “A” represents the actual forces (continuousline) and the reference “D” refers to the instruction expressed by theproposed method (dotted line). FIGS. 13 a-c show the actual and desiredcornering forces of the front axle, rear axle, and the yaw moment of thevehicle.

In FIGS. 13 a-c it can be seen that the saturation of the corneringforces of the front and rear axles and the cornering force delay of therear axle lead to loss of control of the vehicle and to swerving. Thisswerving is also illustrated via the overload in the yaw moment withrespect to the yaw moment desired by the driver. The loss of control ofthe vehicle may be detected wheel by wheel by measuring the differencebetween the instruction cornering forces (described by the formulae(25), (25 bis), (26) and (26 bis)) and the actual cornering forces orthe difference between the instruction loads (described by the formulae(21), (21 bis), (22) and (22 bis)) and the actual loads. FIGS. 14 a, 14b, 14 c, and 14 d show the actual and desired vertical loads Zp on thefour tires. FIGS. 15 a, 15 b, 15 c, and 15 d represent the actual anddesired lateral cornering forces Yp on the four tires.

The fourth simulation (FIGS. 16 a-c, 17 a-d, 18 a-d, 19 and 20) showshow a modification of the front/rear anti-rolling distribution,controlled as explained hereinbefore, enables the path of the vehicle tobe stabilized. In each case the reference “A” represents the actualforces (continuous line) and the reference “D” refers to the instructionexpressed by the proposed method (dotted line). The maneuver isidentical to the preceding maneuver (avoidance maneuver on a wet surfaceat 90 km/hour). As soon as excessive yaw forces are detected theanti-roll device is reinforced at the front of the vehicle and decreasedby the same amount at the rear of the vehicle so as to stabilize thevehicle as quickly as possible and to utilize in the best possible waythe gripping potential of the four tires. The saturation of thecornering forces is handled more effectively and permits smaller phasedifferences, which means that yaw moments are better controlled andmovements of the vehicle body are more easily identified. By means ofthe anti-roll dynamic distribution the system reduces the delay betweenthe driver's instructions to exert the necessary forces and the reactionof the vehicle, and avoids the swerving that is observed in the absenceof the system. FIGS. 16 a, 16 b, and 16 c show the actual and desiredcornering forces of the front axle, rear axle, and the yaw moment of thevehicle. FIGS. 17 a, 17 b, 17 c, and 17 d show the actual and desiredvertical loads Zp on the four tires. FIGS. 18 a, 18 b, 18 c, and 18 dshow the actual and desired lateral cornering forces Yp on the fourtires.

The swerving observed when the vehicle is out of control (FIG. 19,reference numeral 1) is restricted in the presence of the anti-rollcontrol device (FIG. 19, reference numeral 2), which is reflected in analignment of the vehicle parallel to the path of the center of gravity(continuous line).

FIG. 20 illustrates the anti-rolling distribution in order to stabilizethe vehicle. If a saturation is observed, an anti-roll force is exertedon the rear axle in order to increase the front anti-roll whilemaintaining constant the overall anti-roll stiffness. This change indistribution of the loads stabilizes the vehicle by causing it toundersteer more.

1. A method for controlling the stability of a vehicle, the vehiclecomprising a body and at least one front ground contacting arrangementand at least one rear ground contacting arrangement, each groundcontacting arrangement comprising in each case a wheel, each wheelcomprising a tire in contact with the ground, the vehicle having acharacteristic time that is a function of its inertia and corresponds tothe time phase shift in the manifestation of the cornering forces on thewheels in the front and in the rear, following a command from the driverof the vehicle, the vehicle being provided with operating means to acton the forces transmitted to the ground by each of the wheels, themethod comprising the steps of: (a) measuring in real time an actualvalue of one of a cornering force “Y” and a vertical load “Z” acting atthe center of each of the front and rear wheels; (b) calculating in realtime a desired value of at least one reference parameter, said at leastone reference parameter being correlatable to the actual value, as aresult of an action of the driver on the operating means and taking intoaccount the characteristic time; (c) comparing said desired value of thereference parameter of step (b) to the actual value to determine whetherthe actual value is compatible with the desired value of the referenceparameter; and (d) if the comparison of step (c) indicates that theactual value is not compatible, acting on the operating means to bringthe actual value into substantial compatibility with the desired valueof the reference parameter.
 2. A method according to claim 1, whereinsaid variable is the cornering force “Y” and said desired value of atleast one reference parameter of step (b) is the desired cornering force“Y_(desired)” at the center of each wheel.
 3. A method according toclaim 2, wherein step (c) further comprises generating an error signalrepresentative of the magnitude and direction of the difference betweenthe actual cornering force “Y” and the desired cornering force “Y_(d)”;and step (d) comprises controlling said operating means to minimize saiderror signal.
 4. A method according to claim 1 wherein said variable isthe cornering force “Y”, said operating means including a command forcontrolling the steering, and wherein step (a) comprises calculating inreal time an effective yaw moment corresponding to the actual corneringforces “Y” at the center of each wheel, and said desired value of atleast one reference parameter of step (b) is a desired yaw moment, themethod comprising measuring in real time a signal at the steeringcommand and calculating a desired yaw moment “M_(d)”; and step (c)comprises comparing said desired yaw moment “M_(d)” with the effectiveyaw moment of step (a).
 5. A method according to claim 4, wherein step(c) further comprises generating an error signal representative of themagnitude and the direction of the difference between the effective yawmoment and the desired yaw moment “M_(d)”; and step (d) comprisescontrolling said operating means to minimize said error signal. 6.Method for controlling the stability of a vehicle according to claim 1,wherein said variable is the vertical load “Z”.
 7. A method according toclaim 6 wherein said operating means includes a command for controllingthe steering, and wherein said desired value of at least one referenceparameter of step (b) is the desired load “Z_(d)” at the center of eachof wheels, the method including measuring in real time a signal at thesteering command and calculating the desired loads “Z_(d)”.
 8. A methodaccording to claim 7, wherein step (c) further comprises generating anerror signal representative of the magnitude and the direction of thedifference between the actual loads “Z” and the desired loads “Z_(d)”;and step (d) comprises controlling said operating means to minimize saiderror signal.
 9. A method according to claim 1, wherein each groundcontacting arrangement comprises a vertical suspension device allowingclearance of the wheel with respect to the body, first anti-roll controlmeans acting between the wheels of the front axle, second anti-rollcontrol means acting between the wheels of the rear axle, and whereinthe step of acting on the operating means comprises dynamicallymodifying the distribution between the front axle and rear axle of theanti-roll device to maintain a constant overall anti-roll force, beingone of a contribution of the rear anti-roll device being reduced todecrease the yaw moment exerted by the wheels on the vehicle and acontribution of the rear anti-roll device being increased to increasethe yaw moment exerted by the wheels on the vehicle, to reduce the errorsignal.
 10. A method according to claim 1, wherein the vehicle has atleast one axle comprising supplementary means for steering the wheels ofat least one axle, the means acting independently of the steeringcontrol device, wherein the step of acting on the operating meanscomprises dynamically controlling the supplementary steering means tomodify the yaw moment exerted on the vehicle by the wheels to reduce theerror signal.
 11. A method according to claim 1, wherein the vehiclecomprises means for applying a braking torque selectively to each of thewheels, wherein the step of acting on the operating means comprisesexerting one of a braking action on at least one of the wheels outsidethe steering action effected by the vehicle to reduce the yaw momentexerted by the wheels on the vehicle and a braking action on at leastone of the wheels inside the steering action effected by the vehicle toincrease the yaw moment exerted by the wheels on the vehicle to reducethe error signal.
 12. A vehicle stability control system, the vehiclecomprising a body and at least one front ground contacting arrangementand at least one rear ground contacting arrangement, each groundcontacting arrangement comprising a wheel, each wheel comprising a tirein contact with the ground, the vehicle having a characteristic timethat is a function of its inertia and corresponds to the time phaseshift in the manifestation of the cornering forces on the wheels in thefront and in the rear, following a command from the driver of thevehicle, the vehicle being provided with operating means to act on theforces transmitted to the ground by each of the wheels, the systemcomprising: (a) means for measuring in real time actual values of one ofa cornering force “Y” and a vertical load “Z” acting at the center ofeach of the front and rear wheels; (b) a controller for calculating inreal time, as a result of an action of the driver on the operating meansand taking into account the characteristic time, desired values of atleast one reference parameter, said at least one reference parameterbeing correlatable to the actual values, said controller also forcomparing the desired values with the measured actual values in order toobtain an error signal; and, (c) means for acting on the operating meansto minimize the error signal.
 13. A vehicle stability control systemaccording to claim 12, wherein said means for measuring measures actualvalues of the cornering force “Y” and the controller calculates adesired cornering force “Y_(d)” at the center of each wheel.
 14. Avehicle stability control system according to claim 12, wherein saidmeans for measuring measures the cornering force “Y” and the controllercalculates a desired yaw moment “M_(d)”, said operating means includinga command for operating the steering, the system further comprising:means for sensing in real time a signal in the steering command; saidcontroller including means to calculate in real time an effective yawmoment according to said cornering forces “Y” and to calculate thedesired yaw moment “M_(d)” according to the signal in the steeringcommand, the controller allowing to compare the effective and desiredyaw moments in order to obtain said error signal.
 15. A vehiclestability control system according to claim 12, wherein said means formeasuring measures the actual vertical load “Z” and wherein thecontroller calculates the desired vertical load “Z_(d)”.
 16. A vehiclestability control system according to claim 15, wherein said operatingmeans includes a command for operating the steering, the system furthercomprising means for sensing in real time a signal in the steeringcommand, and wherein said controller calculates in real time the actualvertical load “Z” and calculates the desired vertical load “Z_(d)”according to the signal in the steering command, the controller comparesthe effective and desired vertical loads to obtain said error signal.17. A vehicle stability control system according to claim 12, whereineach ground contacting arrangement comprises a vertical suspensiondevice allowing clearance of the wheel with respect to the body, firstanti-roll control means acting between the wheels of the front axle,second anti-roll control means acting between the wheels of the rearaxle, wherein said means for acting on the operating means comprisesmeans for dynamically modifying a distribution between the front axleand rear axle of the anti-roll device so as to maintain a constantoverall anti-roll force, wherein a contribution of the rear anti-rolldevice is decreased to decrease the yaw moment exerted by the wheels onthe vehicle and increased to increase the yaw moment exerted by thewheels on the vehicle, to reduce the error signal.
 18. A vehiclestability control system according to claim 12, wherein the vehicle hasat least one axle comprising supplementary means for steering the wheelsof at least one axle, said means acting independently of the steeringcontrol device, wherein said means for acting on the operating meanscomprises a controller for dynamically controlling the supplementarysteering means to modify the yaw moment exerted on the vehicle by thewheels in order to reduce the error signal.
 19. A vehicle stabilitycontrol system according to claim 12, wherein the vehicle comprisesmeans for applying a braking torque selectively to each of the wheels,and wherein said means for acting on the operating means comprises meansfor selectively exerting a braking action on at least one of the wheelsoutside the steering action effected by the vehicle in order to reducethe yaw moment exerted by the wheels on the vehicle, and exerting abraking action on at least one of the wheels inside the steering actioneffected by the vehicle in order to increase the yaw moment exerted bythe wheels on the vehicle, to reduce the error signal.